80a^3+52a^2-60a=0

Solution for 80a^3+52a^2-60a=0 equation:

Simplifying
80a3 + 52a2 + -60a = 0

Reorder the terms:
-60a + 52a2 + 80a3 = 0

Solving
-60a + 52a2 + 80a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-15 + 13a + 20a2) = 0

Factor a trinomial.
4a((-5 + -4a)(3 + -5a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0
Subproblem 2
Set the factor '(-5 + -4a)' equal to zero and attempt to solve:

Simplifying
-5 + -4a = 0

Solving
-5 + -4a = 0

Move all terms containing a to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -4a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4a = 0 + 5
-4a = 0 + 5

Combine like terms: 0 + 5 = 5
-4a = 5

Divide each side by '-4'.
a = -1.25

Simplifying
a = -1.25
Subproblem 3
Set the factor '(3 + -5a)' equal to zero and attempt to solve:

Simplifying
3 + -5a = 0

Solving
3 + -5a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -5a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5a = 0 + -3
-5a = 0 + -3

Combine like terms: 0 + -3 = -3
-5a = -3

Divide each side by '-5'.
a = 0.6

Simplifying
a = 0.6
Solution
a = {0, -1.25, 0.6}